9-Point Circle Action (Part 3A)
Note: This worksheet follows the 9-Point Circle Action (Part 2) worksheet, which can be found here: https://tube.geogebra.org/m/EHpRBpFE
The applet below contains a triangle shown with its 9-Point Circle and circumcircle. The pink vertices of the triangle are moveable, as well as the BIG WHITE POINT on its circumcircle.
Directions:
1) Select the Midpoint tool in the toolbar. Then select the orthocenter and the BIG WHITE POINT.
This will plot the midpoint of the path (segment) that connects the triangle's orthocenter to this BIG
WHITE POINT on its circumcircle.
2) What do you notice?
3) Now, drag the WHITE POINT around the circumcircle. What do you notice about the midpoint of the path (segment) that connects the triangle's orthocenter to this BIG WHITE POINT on its circumcircle?
4) Given your results for (2) & (3) we can say that triangle's 9-Point Circle is a __________________ of the segment that connects the triangle's orthocenter to any point on its circumcircle.
Note: Feel free to use the segment and/or distance tools to further verify your answers to these
questions listed above.